19,938 research outputs found
Comparison and Rigidity Theorems in Semi-Riemannian Geometry
The comparison theory for the Riccati equation satisfied by the shape
operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds
of arbitrary index, using one-sided bounds on the Riemann tensor which in the
Riemannian case correspond to one-sided bounds on the sectional curvatures.
Starting from 2-dimensional rigidity results and using an inductive technique,
a new class of gap-type rigidity theorems is proved for semi-Riemannian
manifolds of arbitrary index, generalizing those first given by Gromov and
Greene-Wu. As applications we prove rigidity results for semi-Riemannian
manifolds with simply connected ends of constant curvature.Comment: 46 pages, amsart, to appear in Comm. Anal. Geo
A Strong Maximum Principle for Weak Solutions of Quasi-Linear Elliptic Equations with Applications to Lorentzian and Riemannian Geometry
The strong maximum principle is proved to hold for weak (in the sense of
support functions) sub- and super-solutions to a class of quasi-linear elliptic
equations that includes the mean curvature equation for spacelike
hypersurfaces in a Lorentzian manifold. As one application a Lorentzian warped
product splitting theorem is given.Comment: 37 pages, 1 figure, ams-latex using eepi
String Effects on Fermi--Dirac Correlation Measurements
We investigate some recent measurements of Fermi--Dirac correlations by the
LEP collaborations indicating surprisingly small source radii for the
production of baryons in -annihilation at the peak. In the
hadronization models there are besides the Fermi--Dirac correlation effect also
a strong dynamical (anti-)correlation. We demonstrate that the extraction of
the pure FD effect is highly dependent on a realistic Monte Carlo event
generator, both for separation of those dynamical correlations which are not
related to Fermi--Dirac statistics, and for corrections of the data and
background subtractions. Although the model can be tuned to well reproduce
single particle distributions, there are large model-uncertainties when it
comes to correlations between identical baryons. We therefore, unfortunately,
have to conclude that it is at present not possible to make any firm conclusion
about the source radii relevant for baryon production at LEP
Blowup of Jang's equation at outermost marginally trapped surfaces
The aim of this paper is to collect some facts about the blowup of Jang's
equation. First, we discuss how to construct solutions that blow up at an
outermost MOTS. Second, we exclude the possibility that there are extra blowup
surfaces in data sets with non-positive mean curvature. Then we investigate the
rate of convergence of the blowup to a cylinder near a strictly stable MOTS and
show exponential convergence near a strictly stable MOTS.Comment: 15 pages. This revision corrects some typo
A Relativistic Mean Field Model for Entrainment in General Relativistic Superfluid Neutron Stars
General relativistic superfluid neutron stars have a significantly more
intricate dynamics than their ordinary fluid counterparts. Superfluidity allows
different superfluid (and superconducting) species of particles to have
independent fluid flows, a consequence of which is that the fluid equations of
motion contain as many fluid element velocities as superfluid species. Whenever
the particles of one superfluid interact with those of another, the momentum of
each superfluid will be a linear combination of both superfluid velocities.
This leads to the so-called entrainment effect whereby the motion of one
superfluid will induce a momentum in the other superfluid. We have constructed
a fully relativistic model for entrainment between superfluid neutrons and
superconducting protons using a relativistic mean field model
for the nucleons and their interactions. In this context there are two notions
of ``relativistic'': relativistic motion of the individual nucleons with
respect to a local region of the star (i.e. a fluid element containing, say, an
Avogadro's number of particles), and the motion of fluid elements with respect
to the rest of the star. While it is the case that the fluid elements will
typically maintain average speeds at a fraction of that of light, the
supranuclear densities in the core of a neutron star can make the nucleons
themselves have quite high average speeds within each fluid element. The
formalism is applied to the problem of slowly-rotating superfluid neutron star
configurations, a distinguishing characteristic being that the neutrons can
rotate at a rate different from that of the protons.Comment: 16 pages, 5 figures, submitted to PR
The Cosmological Time Function
Let be a time oriented Lorentzian manifold and the Lorentzian
distance on . The function is the cosmological
time function of , where as usual means that is in the causal
past of . This function is called regular iff for all
and also along every past inextendible causal curve. If the
cosmological time function of a space time is regular it has
several pleasant consequences: (1) It forces to be globally hyperbolic,
(2) every point of can be connected to the initial singularity by a
rest curve (i.e., a timelike geodesic ray that maximizes the distance to the
singularity), (3) the function is a time function in the usual sense, in
particular (4) is continuous, in fact locally Lipschitz and the second
derivatives of exist almost everywhere.Comment: 19 pages, AEI preprint, latex2e with amsmath and amsth
Integrable Cosmological Models From Higher Dimensional Einstein Equations
We consider the cosmological models for the higher dimensional spacetime
which includes the curvatures of our space as well as the curvatures of the
internal space. We find that the condition for the integrability of the
cosmological equations is that the total space-time dimensions are D=10 or D=11
which is exactly the conditions for superstrings or M-theory. We obtain
analytic solutions with generic initial conditions in the four dimensional
Einstein frame and study the accelerating universe when both our space and the
internal space have negative curvatures.Comment: 10 pages, 2 figures, added reference, corrected typos(v2),
explanation improved and references and acknowledgments added, accepted for
publication in PRD(v3
Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint Equations
We describe how the iterative technique used by Isenberg and Moncrief to
verify the existence of large sets of non constant mean curvature solutions of
the Einstein constraints on closed manifolds can be adapted to verify the
existence of large sets of asymptotically hyperbolic non constant mean
curvature solutions of the Einstein constraints.Comment: 19 pages, TeX, no figure
Stability of the r-modes in white dwarf stars
Stability of the r-modes in rapidly rotating white dwarf stars is
investigated. Improved estimates of the growth times of the
gravitational-radiation driven instability in the r-modes of the observed DQ
Her objects are found to be longer (probably considerably longer) than 6x10^9y.
This rules out the possibility that the r-modes in these objects are emitting
gravitational radiation at levels that could be detectable by LISA. More
generally it is shown that the r-mode instability can only be excited in a very
small subset of very hot (T>10^6K), rather massive (M>0.9M_sun) and very
rapidly rotating (P_min<P<1.2P_min) white dwarf stars. Further, the growth
times of this instability are so long that these conditions must persist for a
very long time (t>10^9y) to allow the amplitude to grow to a dynamically
significant level. This makes it extremely unlikely that the r-mode instability
plays a significant role in any real white dwarf stars.Comment: 5 Pages, 5 Figures, revte
R-mode oscillations and rocket effect in rotating superfluid neutron stars. I. Formalism
We derive the hydrodynamical equations of r-mode oscillations in neutron
stars in presence of a novel damping mechanism related to particle number
changing processes. The change in the number densities of the various species
leads to new dissipative terms in the equations which are responsible of the
{\it rocket effect}. We employ a two-fluid model, with one fluid consisting of
the charged components, while the second fluid consists of superfluid neutrons.
We consider two different kind of r-mode oscillations, one associated with
comoving displacements, and the second one associated with countermoving, out
of phase, displacements.Comment: 10 page
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